To solve for \( u \) in the equation
\[ 35 = -\frac{7}{3} u, \]
we first want to isolate \( u \). We can do this by multiplying both sides of the equation by the reciprocal of \(-\frac{7}{3}\), which is \(-\frac{3}{7}\):
\[ u = 35 \cdot -\frac{3}{7}. \]
Now let's simplify the right side:
- Multiply 35 by -3:
\[ 35 \cdot -3 = -105. \]
- Then divide \( -105 \) by 7:
\[ -\frac{105}{7} = -15. \]
Putting it all together, we find:
\[ u = -15. \]
Therefore, the solution for \( u \) is
\[ \boxed{-15}. \]
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